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Associate Professor of Photonics and Quantum Sciences, Heriot-Watt University

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Michael Hartmann does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

British scientists David Thouless, Duncan Haldane and Michael Kosterlitz won this year’s Nobel Prize in Physics “for theoretical discoveries of topological phase transitions and topological phases of matter”. The reference to “theoretical discoveries” makes it tempting to think their work will not have practical applications or affect our lives some day. The opposite may well be true.

To understand the potential, it helps to understand the theory. Most people know that an atom has a nucleus in the middle and electrons orbiting around it. These correspond to different energy levels. When atoms group into substances, all the energy levels of each atom combine into bands of electrons. Each of these so-called energy bands has space for a certain number of electrons. And between each band are gaps in which electrons can’t flow.

If you apply an electrical charge (a flow of extra electrons) to a material, its conductivity is determined by whether the highest energy band has room for more electrons. If it does have room, the material will behave as a conductor. If not, you need extra energy to push the current of electrons into a new empty band and as a result the material behaves as an insulator. Understanding conductivity is vital to electronics, since electronic products ultimately rely on components that are electric conductors, semiconductors and insulators.

What Thouless, Haldane and Kosterlitz began to predict in the 1970s and 1980s and other theorists have since taken forward is that certain materials break this rule. Instead of having a gap between bands in which electrons can’t flow, they have a special energy level between their bands where certain unexpected things are possible.

This quality only exists on the surface or edge of these materials, and is very robust. It also depends to some extent on the shape of the material – the topology, as we say in physics. It behaves identically for a sphere and an egg, for example, but would be different for something shaped like a doughnut because of the hole in the middle. The first measurements of this kind of behaviour have been taken for a current along the boundary of a flat sheet.

Thouless, Haldane and Kosterlitz.

Computer power

The properties of these so-called topological materials could potentially be extremely useful. Electrical currents can move without resistance across their surface, for example, even where a device is moderately damaged. Superconductors can already do this without having topological properties, but they only work at very low temperatures – meaning you use a lot of energy keeping them cool. Topological materials have the potential to do the same job at higher temperatures.

This has important implications for computing: most of the energy computers currently use is to run ventilators to cool down the heat produced by electrical resistance in the circuits. Remove this heat problem and you potentially make them many times more energy efficient. This could massively reduce their carbon emissions, for instance. It could also lead to batteries with far longer life spans. Researchers are already experimenting with topological materials like cadmium telluride and mercury telluride to bring this vision to life.

There is also the potential for a major breakthrough in quantum computing. Classical computers encode information by either applying voltage or not applying voltage to a chip. The computer reads this as a 0 or 1 respectively for each “bit” of information. You put these bits together to build up more complex information. This is how the binary system works.

With quantum computing, you deliver information to electrons instead of microchips. The energy levels of these electrons then correspond to zeros and ones just like in classical computers, but in quantum mechanics both can be true at the same time. Without getting into too much theory, this raises the possibility of computers that can process exceedingly large amounts of data in parallel and are therefore much faster.

While the likes of Google and IBM are researching how to manipulate enough electrons to create quantum computers that are more powerful than classical computers, one big obstacle is that these computers are very fragile with respect to surrounding “noise”. Whereas classical computers can cope with interference, quantum computers end up producing intolerable numbers of errors because of shaky support frames, stray electrical fields or air molecules hitting the processor even if you hold it in a high vacuum. This is the main reason why we don’t yet use quantum computers in our everyday lives.

One potential solution is to store information in more than one electron, since noise typically affects quantum processors at the level of single particles. Supposing you have five electrons all jointly storing the same bit of information, so long as the majority store it correctly, a disturbance to a single electron won’t undermine the system.

Researchers have been experimenting with this so-called majority voting, but topological engineering potentially offers an easier fix. In the same way as topological superconductors can carry a flow of electricity well enough that it doesn’t get hampered by resistance, topological quantum processors could be robust enough to be insensitive to noise problems. They could yet offer a major contribution to making quantum computing a reality. Researchers in the US are working on it.

The future

It might take between ten and 30 years before scientists become sufficiently good at manipulating electrons to make quantum computing possible, but they open up exciting possibilities. They could simulate the formation of molecules, for example, which is numerically too complicated for today’s computers. This could revolutionise drug research by enabling us to predict what will happen during chemical processes in the body.

To give just one other example, quantum computing has the potential to make artificial intelligence a reality. Quantum machines may be better at learning than classical computers, partly because they might be underpinned by much cleverer algorithms. Cracking AI could be a step change in human existence – for better or worse.

In short, the predictions of Thouless, Haldane and Kosterlitz have the potential to help revolutionise 21st-century computer technology. Where the Nobel committee has recognised the importance of their work in 2016, we are likely to be thanking them many decades into the future.